Legendre's Conjecture
Jump to navigation
Jump to search
Open Question
It is not known whether:
- $\exists n \in \N_{>1}: \map \pi {n^2 + 2 n + 1} = \map \pi {n^2}$
where $\pi$ denotes the prime-counting function.
That is:
- Is there always a prime number between consecutive squares?
Source of Name
This entry was named for Adrien-Marie Legendre.
Landau's Problems
This is the $3$rd of Landau's problems.
Sources
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.1$: Functions: Example $2.1.1$